1986 Yamaha Moto 4
 

ATV is in good shape but won't idle and is fouling plug. Also bogs out sometimes and backfires......any ideas???

Sounds like you should start by taking the carb out, cleaning it and making sure the float is set, along with a new needle and seat, you can get a rebuild kit, that usually has the needle and seat in it, with the gaskets you need.
I had an 86 Moto 4, it had a rusted choke plate, but after cleaning the carb and setting the valves, it ran like a Swiss watch, would start in below zero weather easily, and idled smooth and quiet.